Analytic and Bootstrap-after-Cross-Validation Methods for Selecting Penalty Parameters of High-Dimensional M-Estimators

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We develop two new methods for selecting the penalty parameter for the `1-penalized high-dimensional M-estimator, which we refer to as the analytic and bootstrap-aftercross-validation methods. For both methods, we derive nonasymptotic error bounds for the corresponding `1-penalized M-estimator and show that the bounds converge to zero under mild conditions, thus providing a theoretical justification for these methods. We demonstrate via simulations that the finite-sample performance of our methods is much better than that of previously available and theoretically justified methods.
Original languageEnglish
Number of pages63
Publication statusPublished - 10 Apr 2021
SeriesUniversity of Copenhagen. Institute of Economics. Discussion Papers (Online)

    Research areas

  • Faculty of Social Sciences - penalty parameter selection, penalized M-estimation, high-dimentional models, sparsity, cross-validation, bootstrap


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